Local Smoothness in Terms of Variance: The Adaptive Gaussian Filter

Several techniques, such as adaptive smoothing [9, 10] or anisotropic diusion [4, 5] deal with the task of local smoothing. That is, preserv-ing principal discontinuities and smoothing within regions. Unfortu-nately, these types of iterative techniques have as one of their main drawbacks, the determination of the threshold on the luminance gradi-ent. There is no way to control it easily and researchers often fall into a trial-and-error procedure. In this paper an adaptive Gaussian l-ter that computes directly the local amount of Gaussian smoothing in terms of variance is presented. The local variance, (x; y), is selected, in a scale-space framework, through the minimal description length criterion (MDL). The MDL allows us to estimate the local smoothing in such a way that it respects the main discontinuities. The resulting smoothed image, in location x; y, is the intensity given by the convo-lution of the initial point I 0 (x; y) with its appropriate Gaussian kerne